Computation of the one-dimensional unwrapped phase

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 101-102). "Cepstrum bibliography" (p. 67-100).In this thesis, the computation of the unwrapped phase of the discrete-time Fourier transform (DTFT) of a one-dimensional finite-length signal is explored. The phase of the DTFT is not unique, and may contain integer multiple of 27r discontinuities. The unwrapped phase is the instance of the phase function chosen to ensure continuity. This thesis presents existing algorithms for computing the unwrapped phase, discussing their weaknesses and strengths. Then two composite algorithms are proposed that use the existing ones, combining their strengths while avoiding their weaknesses. The core of the proposed methods is based on recent advances in polynomial factoring. The proposed methods are implemented and compared to the existing ones.by Zahi Nadim Karam.S.M

Phase Space Analysis and Classification of Sonar Echoes in Shallow-Water Channels

A primary objective of active sonar systems is to detect, locate, and classify objects, such as mines, ships, and biologics, based on their sonar backscatter. A shallow-water ocean channel is a challenging environment in which to classify sonar echoes because interactions of the sonar signal with the ocean surface and bottom induce frequency-dependent changes (especially dispersion and damping) in the signal as it propagates, the effects of which typically grow with range. Accordingly, the observed signal depends not only on the initial target backscatter, but also the propagation channel and how far the signal has propagated. These propagation effects can increase the variability of observed target echoes and degrade classification performance. Furthermore, uncertainty of the exact propagation channel and random variations within a channel cause classification features extracted from the received sonar echo to behave as random variables.With the goal of improving sonar signal classification in shallow-water environments, this work develops a phase space framework for studying sound propagation in channels with dispersion and damping. This approach leads to new moment features for classification that are invariant to dispersion and damping, the utility of which is demonstrated via simulation. In addition, the accuracy of a previously developed phase space approximation method for range-independent pulse propagation is analyzed and shown to be greater than the accuracy of the standard stationary phase approximation for both large and small times/distances. The phase space approximation is also extended to range dependent propagation. Finally, the phase space approximation is used to investigate the random nature of moment features for classification by calculating the moments of the moment features under uncertain and random channel assumptions. These moments of the moment features are used to estimate probability distribution functions for the moment features, and we explore several ways in which this information may be used to improve sonar classification performance